Mrykx,
What you discribe is very similar to what we have on our 43. We have done the work while in the water without issue, but caution is advised. What I found was that the leakage was minimal and perhaps flowed at a rate of a couple of gallons every 1/2 hour.
The issue with time is having the correct packing and then precutting as Mike discribes. I was surprised to find that the previous own had placed a single ring of 1/4" packing around the shaft and then forced the nut back over the packing. Essentially it worked, but once the packing began to wear (or heat) you could not stop the dripping with any amount of force on the nut. Ultimately I had to leave the disabled stuffing tube open for about an hour or so while I ran to West Marine for 3/16" and 1/8" packing material. If you have never done this before I would suggest you pickup each size and have it available before you start the job. Return what you don't need, it is cheap anyway.
Our set up works very similar to Mikes discription in that the rings go around the shaft and are slipped into the tube, not into the nut. If I recall correctly 3-4 rings filled the lateral space, and 1/8" material was correct for fitting between the shaft and the tube.
Most likely best to be sure you bilge pump is operating correctly, if you really come up against any trouble you can always re-assemble what you have an limit the sinking factor
